DCT 90102: Econometric Methods for Business Research I DCT 90102: Econometric Methods for Business Research I Sebastiano Manzan, Fall 2021 Assignment 2: Linear Regression model for CEO compensation •...

This assignment needs to be completed in R.


DCT 90102: Econometric Methods for Business Research I DCT 90102: Econometric Methods for Business Research I Sebastiano Manzan, Fall 2021 Assignment 2: Linear Regression model for CEO compensation • The weight of this problem set is 10% of the overall grade • The problem set is done individually, but you can discuss it with other students • The assignment should be completed in R • Create a Word document that contains a section for each question and copy the tables and graphs produced in R. Provide also a discussion of the results • Submit the Word file in Blackboard under Assignment 2 by 8.30am on Friday December 3, 2021 In this second assignment we will use again the CEO compensation dataset for 2016 that was analyzed in the first assignment and where you can find the description of the variables. There is quite a lot of dispersion in TDC1 with 9 CEOs receiving less than 100 thousand dollars in TDC1 in 2016 while 9 others receiving more than 35 million dollars. The goal of this assignment is to answer the following questions: which factors explain the variability across CEOs in their compensation? Q1. (20%) Let’s consider first ASSETS as a potential factor explaining TDC1 and assume that there is a linear relationship between the two variables: TDC1i = β0 + β1 ∗ ASSETSi + ui Estimation of β0 and β1 requires to calculate the average and standard deviation of TDC1 and ASSETS and the covariance or correlation between ASSETS and TDC1. The formulas are: • b2 = cov(T DC1i,ASSET Si)σ2ASSET S or b2 = cor(T DC1i,ASSET Si)σT DC1 σASSET S • b1 = TDC1 − b2 ∗ ASSETS • Calculate b1 and b2 and provide an interpretation of the estimated values Q2. (20%) 1 • Scatter plot TDC1 against ASSETS together with the regression line using ‘ggplot2 and adding geom_abline(intercept = b1, slope = b2) command. Discuss the fitness of the regres- sion line to account for the relationship between company’s total assets and CEO compensa- tion. Q3. (20%) Estimate the linear regression model using the lm() function in R with code fit <- lm(tdc1="" ~="" assets,="" data="ceo.data)" and="" then="" print="" the="" output="" using="" summary(fit)="" (or="" whatever="" name="" you="" gave="" the="" output="" of="" the="" lm()="" function).="" •="" is="" assets="" a="" statistically="" significant="" variable="" to="" explain="" tdc1?="" test="" the="" null="" hypothesis="" that="" β1="0" against="" the="" alternative="" that="" is="" different="" from="" zero="" at="" 5%="" significance="" level.="" q4.="" (20%)="" how="" good="" is="" the="" regression="" model="" with="" assets="" as="" the="" independent="" variable="" to="" explain="" tdc1?="" discuss="" the="" r2="" provided="" in="" the="" output="" of="" the="" lm()="" function.="" q5.="" (20%)="" assets="" is="" one="" of="" several="" factors="" available="" in="" the="" dataset="" that="" can="" explain="" tdc1.="" estimate="" the="" linear="" regression="" model="" with="" assets="" and="" ni="" (net="" income)="" as="" independent="" variables="" using="" the="" command="" fit=""><- lm(tdc1 ~ assets + ni, data=ceo.data). print the summary of the fit object and discuss: • the statistical significance of the assets and ni variables at 5% level • did the significance of assets change when ni is added to the regression? why? • did the goodness of the regression model improve by adding ni? 2 assignment 2: linear regression model for ceo compensation lm(tdc1="" ~="" assets="" +="" ni,="" data="ceo.data)." print="" the="" summary="" of="" the="" fit="" object="" and="" discuss:="" •="" the="" statistical="" significance="" of="" the="" assets="" and="" ni="" variables="" at="" 5%="" level="" •="" did="" the="" significance="" of="" assets="" change="" when="" ni="" is="" added="" to="" the="" regression?="" why?="" •="" did="" the="" goodness="" of="" the="" regression="" model="" improve="" by="" adding="" ni?="" 2="" assignment="" 2:="" linear="" regression="" model="" for="" ceo="">